Choosing paper: kami, washi and printer paper
Kami
The standard square origami paper: thin, coloured on one side, cheap. Holds sharp creases and is the right choice for learning and for most traditional models.
Washi
Long fibres make it strong and soft. It does not take a crisp crease as easily, but it is ideal for wet-folding and for models that should look rounded rather than geometric.
Printer paper
Too thick for complex bases, but perfectly fine for boxes, envelopes and practising basic folds. Cut it square carefully: a crooked square is the most common reason a model will not close.